Sparse Fourier restriction for the cone

In Fourier restriction theory, weighted inequalities allow us to probe the shape of level sets. In this thesis, we describe a new weighted Fourier extension estimate for the cone and its connection with the Mizohata–Takeuchi conjecture. The main result Theorem 3.1 builds on techniques from geometry originally explored by Tom Wolff in this context. The proof uses circular maximal function estimates first proved by Wolff and later generalized by Pramanik–Yang–Zahl in their work on restricted projections as a black box.

Name thesis:degree_name

Doctoral

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Mathematics

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2024

Author dc:creator

• Ortiz, Alexander

Advisor dc:contributor.advisor

• Guth, Lawrence

Statement dc:rights

• Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
• Copyright retained by author(s)

Licence dc:rights.uri

• https://creativecommons.org/licenses/by-nc-nd/4.0/

Handle dc:identifier.uri

https://hdl.handle.net/1721.1/155321

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/155321